We present diffraction limited spectroscopic observations of an infrared flare associated with the radio source SgrA*. These are the first results obtained with OSIRIS, the new facility infrared imaging spectrograph for the Keck Observatory operated with the laser guide star adaptive optics system. After subtracting the spectrum of precursor emission at the location of Sgr A*, we find the flare has a spectral index (F( nu ) \propto nu alpha ) of alpha = -2.6 +/- 0.9. If we do not subtract the precursor light, then our spectral index is consistent with earlier observations by Ghez et al. (2005). All observations published so far suggest that the spectral index is a function of the flare's K-band flux.